Answer to April 7, 2003 Problem |
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The Stagecoach Problem Besides writing Alice In Wonderland, Lewis Carroll composed many puzzles, some of which he recorded in his notebooks without solutions. The following is one such puzzle:"A stagecoach leaves London for York and another at the same moment leaves York for London. They go at uniform rates, one faster than the other. After meeting and passing, one requires sixteen hours and the other nine hours to complete the journey. What total time does each coach require for the whole journey?" Can you solve the problem?
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Solution to Problem: One coach requires 21 hours, the other 28 hours.
Let t represent the time from the coaches'
departure until they pass each other. Then t + 9
is the total time for one coach's trip and t + 16 is
the total time for the other's. Richard Johnson sent in an excellent analysis of the problem:
T= time to meet
D1 = Rf * 9 = Rs * T
T = Rf * 9 / Rs = Rs * 16 / Rf
D1 = Rf * 9 = Rs * T
Fast one = 9 + 12 = 21 hours
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1. Bob Hearn | Winchester, Virginia |
2. Richard Johnson | La Jolla, California |
3. Andrea Eberhard | Columbus, Ohio |
4. Rick Jones | Kennett Square, Pennsylvania |
5. Josh Feingold | Winchester, Virginia |
6. James Alarie | University of Michigan -- Flint Flint, Michigan |
7. Tina Zahel | Winchester, Virginia |
8. David & Judy Dixon | Bennettsville, South Carolina |
9. Michael Rodriguez | Great Falls, Montana |
10. David Brooks | Franklin, Tennessee |